where we have used \(P_{1}^{\prime z}=P_{A1}^{z}\)  as the solution
to the energy conservation equation with the conditions \(\mathbf {P}_{1T}=\mathbf {P}_{1T}^{\prime }\) 
and \(\mathbf {P}_{2T}=\mathbf {P}_{2T}^{\prime }\) . The result of (REF )
is consistent with the results in Ref. [1]}, [2]}.
